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<h1><img src="../../../../boost.png" alt="boost.png (6897 bytes)" align=
"middle" width="277" height="86">Boost.MultiIndex Index reference</h1>

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<h2>Contents</h2>

<ul>
  <li><a href="#index_concepts">Index concepts</a></li>
  <li><a href="#complexity_signature">Complexity signature</a></li>
  <li><a href="#index_specification">Index specification</a></li>
  <li><a href="#indexed_by_synopsis">Header
    <code>"boost/multi_index/indexed_by.hpp"</code> synopsis</a>
    <ul>
      <li><a href="#indexed_by">Class template <code>indexed_by</code></a></li>
    </ul>
  </li>
  <li><a href="#tags">Tags</a></li>
  <li><a href="#tag_synopsis">Header
    <code>"boost/multi_index/tag.hpp"</code> synopsis</a>
    <ul>
      <li><a href="#tag">Class template <code>tag</code></a></li>
    </ul>
  </li>
  <li><a href="#index_catalog">Indices provided by Boost.MultiIndex</a>
    <ul>
      <li><a href="#key_based_indices">Key-based indices</a></li>
      <li><a href="#other_indices">Other types</a></li>
    </ul>
  </li>
  <li><a href="#views">Index views</a></li>
</ul>

<h2><a name="index_concepts">Index concepts</a></h2>

<p>
<code>multi_index_container</code> instantiations comprise one or more indices
specified at compile time. Each index allows read/write access to the elements
contained in a definite manner. For instance,
<a href="ord_indices.html">ordered indices</a>
provide a set-like interface to the elements, whereas
<a href="seq_indices.html">sequenced indices</a> mimic the functionality
of <code>std::list</code>.
</p>

<p>
Indices are not isolated objects, and so cannot be constructed on their
own. Rather they are embedded into a <code>multi_index_container</code> as specified by
means of an <a href="#index_specification">index specifier</a>. The name of
the index class implementation proper is never directly exposed to the user, who
has only access to the associated index specifier.
</p>

<p>
Insertion and erasing of elements are always performed through the
appropriate interface of some index of the <code>multi_index_container</code>;
these operations, however, do have an impact on all other indices as
well: for instance, insertion through a given index may fail because
there exists another index which bans the operation in order to preserve
its invariant (like uniqueness of elements.) This circumstance, rather
than being an obstacle, yields much of the power of Boost.MultiIndex:
equivalent constructions based on manual composition of standard
containers would have to add a fair amount of code in order to
globally preserve the invariants of each container while guaranteeing
that all of them are synchronized. The global operations performed
in a joint manner among the various indices can be reduced to
six primitives:
<ul>
  <li>Copying,</li>
  <li>insertion of an element,</li>
  <li>hinted insertion, where a preexisting element is suggested in
    order to improve the efficiency of the operation,</li>
  <li>deletion of an element,</li>
  <li>replacement of the value of an element,
    which may trigger the rearrangement of this element in one or
    more indices, or the banning of the replacement,</li>
  <li>modification of an element, and its subsequent
    rearrangement/banning by the various indices.
</ul>
The last two primitives deserve some further explanation: in order to
guarantee the invariants associated to each index (e.g. some definite
ordering,) elements of a <code>multi_index_container</code> are not mutable.
To overcome this restriction, indices expose member functions
for replacement and modification which allow for the mutation of elements
in a controlled fashion. Immutability of elements does not significantly
impact the interfaces of ordered and hashed indices, as they are based upon
those of associative and unordered associative containers, respectively,
and these containers
also have non-mutable elements; but it may come as a surprise when dealing
with sequenced and random access indices, which are designed upon the functionality provided
by <code>std::list</code>. 
</p>

<p>
These global operations are not directly exposed to the user, but rather
they are wrapped as appropriate by each index (for instance, ordered indices
provide a set-like suite of insertion member functions, whereas sequenced
and random access indices have <code>push_back</code> and <code>push_front</code>
operations.) Boost.MultiIndex poses no particular conditions on
the interface of indices, although each index provided satisfy the C++ requirements for
standard containers to the maximum extent possible within the conceptual framework
of the library.
</p>

<h2><a name="complexity_signature">Complexity signature</a></h2>

<p>
Some member functions of an index interface are implemented by
global primitives from the list above. Complexity of these operations
thus depends on all indices of a given <code>multi_index_container</code>, not just
the currently used index.
</p>

<p>
In order to establish complexity estimates, an index is characterized
by its <i>complexity signature</i>, consisting of the following
associated functions on the number of elements:
<ul>
  <li><code>c(n)</code>: copying,
  <li><code>i(n)</code>: insertion,
  <li><code>h(n)</code>: hinted insertion,
  <li><code>d(n)</code>: deletion,
  <li><code>r(n)</code>: replacement,
  <li><code>m(n)</code>: modifying.
</ul>

</p>
Each function yields the complexity estimate of the contribution of the index
to the corresponding global primitive. Let us consider
an instantiation of <code>multi_index_container</code>
with <code>N</code> indices labelled <code>0</code>,...,<code>N-1</code>
whose complexity signatures are
(<code>c<sub>i</sub></code>,<code>i<sub>i</sub></code>,<code>h<sub>i</sub></code>,<code>d<sub>i</sub></code>,<code>r<sub>i</sub></code>,<code>m<sub>i</sub></code>);
the insertion of an element in such a container is then of complexity
<code>O(i<sub>0</sub>(n)+&middot;&middot;&middot;+i<sub>N-1</sub>(n))</code> where <code>n</code>
is the number of elements. To abbreviate notation, we adopt the
following definitions:
<ul>
  <li><code>C(n)=c<sub>0</sub>(n)+&middot;&middot;&middot;+c<sub>N-1</sub>(n)</code>,</li>
  <li><code>I(n)=i<sub>0</sub>(n)+&middot;&middot;&middot;+i<sub>N-1</sub>(n)</code>,</li>
  <li><code>H(n)=h<sub>0</sub>(n)+&middot;&middot;&middot;+h<sub>N-1</sub>(n)</code>,</li>
  <li><code>D(n)=d<sub>0</sub>(n)+&middot;&middot;&middot;+d<sub>N-1</sub>(n)</code>,</li>
  <li><code>R(n)=r<sub>0</sub>(n)+&middot;&middot;&middot;+r<sub>N-1</sub>(n)</code>,</li>
  <li><code>M(n)=m<sub>0</sub>(n)+&middot;&middot;&middot;+m<sub>N-1</sub>(n)</code>.</li>
</ul>
For instance, consider a <code>multi_index_container</code> with two ordered indices,
for which <code>i(n)=log(n)</code>, and a sequenced index with <code>i(n)=1</code>
(constant time insertion). Insertion of an element into this <code>multi_index_container</code>
is then of complexity
<blockquote>
<code>O(I(n))=O(2*log(n)+1)=O(log(n))</code>.
</blockquote>
</p>

<h2><a name="index_specification">Index specification</a></h2>

<p>
Index specifiers are passed as instantiation arguments to
<code>multi_index_container</code> and provide the information needed to incorporate
the corresponding indices. Future releases of Boost.MultiIndex may allow for
specification of user-defined indices. Meanwhile, the requirements for an index
specifier remain implementation defined. Currently, Boost.MultiIndex provides the
index specifiers
<ul>
  <li><a href="ord_indices.html#unique_non_unique"><code>ordered_unique</code> and
    <code>ordered_non_unique</code></a> for
    <a href="ord_indices.html">ordered indices</a>,</li>
  <li><a href="rnk_indices.html#unique_non_unique"><code>ranked_unique</code> and
    <code>ranked_non_unique</code></a> for
    <a href="rnk_indices.html">ranked indices</a>,</li>
  <li><a href="hash_indices.html#unique_non_unique"><code>hashed_unique</code> and
    <code>hashed_non_unique</code></a> for
    <a href="hash_indices.html">hashed indices</a>,</li>
  <li><a href="seq_indices.html#sequenced"><code>sequenced</code></a> for
    <a href="seq_indices.html">sequenced indices</a>,</li>
  <li>and <a href="rnd_indices.html#random_access"><code>random_access</code></a> for
    <a href="rnd_indices.html">random access indices</a>.</li>
</ul>
</p>

<h2>
<a name="indexed_by_synopsis">Header
<a href="../../../../boost/multi_index/indexed_by.hpp">
<code>"boost/multi_index/indexed_by.hpp"</code></a> synopsis</a></h2>

<blockquote><pre>
<span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

<span class=keyword>namespace</span> <span class=identifier>multi_index</span><span class=special>{</span>

<span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>T0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Tn</span><span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=identifier>indexed_by</span><span class=special>;</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index</span> 

<span class=special>}</span> <span class=comment>// namespace boost</span>
</pre></blockquote>

<h3><a name="indexed_by">Class template <code>indexed_by</code></a></h3>

<p>
<code>indexed_by</code> is a model of
<a href="../../../../libs/mpl/doc/refmanual/random-access-sequence.html">
<code>MPL Random Access Sequence</code></a> and
<a href="../../../../libs/mpl/doc/refmanual/extensible-sequence.html">
<code>MPL Extensible Sequence</code></a> meant to be used to specify a
compile-time list of indices as the <code>IndexSpecifierList</code> of
<code>multi_index_container</code>.
</p>

<blockquote><pre>
<span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>T0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Tn</span><span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=identifier>indexed_by</span><span class=special>;</span>
</pre></blockquote>

<p>
Each user-provided element of <code>indexed_list</code> must be an index
specifier. At least an element must be provided. The maximum number of elements
of an <code>indexed_by</code> sequence is implementation defined.
</p>

<h2><a name="tags">Tags</a></h2>

<p>
Tags are just conventional types used as mnemonics for indices of an
<code>multi_index_container</code>, as for instance in member function <code>get</code>.
Each index can have none, one or more tags associated. The way tags are assigned
to a given index is dependent on the particular index specifier. However,
for convenience all indices of Boost.MultiIndex support tagging through the
class template <a href="#tag"><code>tag</code></a>.
</p>

<h2>
<a name="tag_synopsis">Header
<a href="../../../../boost/multi_index/tag.hpp">
<code>"boost/multi_index/tag.hpp"</code></a> synopsis</a></h2>

<blockquote><pre>
<span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

<span class=keyword>namespace</span> <span class=identifier>multi_index</span><span class=special>{</span>

<span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>T0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Tn</span><span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=identifier>tag</span><span class=special>;</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index</span> 

<span class=special>}</span> <span class=comment>// namespace boost</span>
</pre></blockquote>

<h3><a name="tag">Class template <code>tag</code></a></h3>

<p>
<code>tag</code> is a typelist construct used to specify a compile-time
sequence of tags to be assigned to an index in instantiation time.
</p>

<blockquote><pre>
<span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>T0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Tn</span><span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=identifier>tag</span>
<span class=special>{</span>
  <span class=keyword>typedef</span> <b>implementation defined</b> <span class=identifier>type</span><span class=special>;</span>
<span class=special>};</span>
</pre></blockquote>

<p>
Elements of <code>tag</code> can be any type, though the user is expected
to provide classes with mnemonic names. Duplicate elements are not allowed.
The maximum number of elements of a <code>tag</code> instantiation is
implementation defined.
The nested
<code>type</code> is a model of
<a href="../../../../libs/mpl/doc/refmanual/random-access-sequence.html">
<code>MPL Random Access Sequence</code></a> and
<a href="../../../../libs/mpl/doc/refmanual/extensible-sequence.html">
<code>MPL Extensible Sequence</code></a> containing the types <code>T0</code>, ... ,
<code>Tn</code> in the same order as specified.
</p>

<h2><a name="index_catalog">Indices provided by Boost.MultiIndex</a></h2>


<h3><a name="key_based_indices">Key-based indices</a></h3>

<p>
Indices of this type are organized around <i>keys</i> obtained from the
elements, as described in the <a href="key_extraction.html">key extraction
reference</a>.
<ul>
  <li><a href="ord_indices.html">Ordered indices</a> sort the elements
    on the key and provide fast lookup capabilites.</li>
  <li><a href="rnk_indices.html">Ranked indices</a> are a variation of
    ordered indices providing extra operations based on 
    <i>rank</i>, the numerical position of an element
    in the sequence.</li>
  <li><a href="hash_indices.html">Hashed indices</a> offer high
    efficiency access through hashing techniques.</li>
</ul>
</p>

<h3><a name="other_indices">Other types</a></h3>

<p>
<ul>
  <li><a href="seq_indices.html">Sequenced indices</a> allow to arrange
    elements as in a bidirectional list.</li>
  <li><a href="rnd_indices.html">Random access indices</a> provide
    constant time positional access and free ordering of elements.</li>
</ul>
</p>

<h2><a name="views">Index views</a></h2>

<p>
The following concept is used by the rearrange facilities of non key-based
indices. Given an index <code>i</code> of type <code>Index</code>, a <i>view
of <code>i</code></i> is any range [<code>first</code>,<code>last</code>)
where <code>first</code> and <code>last</code> are input iterators such that
<ol>
  <li>the associated value type of <code>Iterator</code> is convertible
    to <code>const Index::value_type&amp;</code>
  </li>
  <li>and each of the elements of <code>i</code> appears exactly once in
    [<code>first</code>,<code>last</code>).
  </li>
</ol>
Note that the view refers to the actual elements of <code>i</code>, not to
copies of them. Additionally, a view is said to be <i>free</i> if its traversal
order is not affected by changes in the traversal order of <code>i</code>.
Examples of free views are:
<ul>
  <li>[<code>c.begin()</code>,<code>c.end()</code>), where <code>c</code> is
    any container of reference wrappers (from
    <a href="../../../../doc/html/ref.html">Boost.Ref</a>) to the elements
    of <code>i</code> containing exactly one reference to every element.
  </li>
  <li>[<code>i'.begin()</code>,<code>i'.end()</code>), where <code>i'</code> is
    any index belonging to the same <code>multi_index_container</code>
    as <code>i</code>, except <code>i</code> itself.
  </li>
  <li>
    Any range which is a permutation of the ones described above, as for
    instance [<code>c.rbegin()</code>,<code>c.rend()</code>), or
    ranges obtained from the former with the aid of
    <a href="../../../../libs/iterator/doc/permutation_iterator.html">
    <code>permutation_iterator</code></a> from Boost.Iterator.
  </li>
</ul>
</p>

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<br>

<p>Revised January 9th 2020</p>

<p>&copy; Copyright 2003-2020 Joaqu&iacute;n M L&oacute;pez Mu&ntilde;oz.
Distributed under the Boost Software 
License, Version 1.0. (See accompanying file <a href="../../../../LICENSE_1_0.txt">
LICENSE_1_0.txt</a> or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
http://www.boost.org/LICENSE_1_0.txt</a>)
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